City were given a stern test on a wet and windy night at a noisy Kassam Stadium but two goals from Raheem Sterling eventually saw them through.
A night of wholesale team changes for the 11 Premier League sides in action produced one notable upset with top flight Stoke City losing 2-0 at second-tier Bristol City.
Wright blasts Man City's Haaland for throwing ball at Arsenal's Gabriel
Trailing 1-0 from the semi-final first leg, Chelsea turned the tie on its head with goals by N'Golo Kante and Eden Hazard in the first half but Fernando Llorente struck for Spurs in an enthralling Stamford Bridge duel.
On a crazy evening it looked as though Joe Willock's screamer had earned Arsenal a memorable victory, but Liverpool proved irrepressible as their barnstorming season continued.
Bristol City, from English football's second-tier, pulled off a sensation in the League Cup quarter-finals as they knocked out the holders Manchester United 2-1 amid late and wholly improbable drama at their Ashton Gate home on Wednesday.
Seb Larsson's late strike sent struggling Sunderland through to the League Cup quarter-finals with a 2-1 win over fellow Premier League side Southampton on Wednesday.
Manchester City won the English League Cup for the second successive season as the beat Chelsea 4-3 in a penalty shootout after the Wembley showpiece had ended 0-0 after extra time.
Burnley beat Blackburn Rovers 2-0 at Ewood Park in their East Lancashire derby but Premier League sides Southampton and Newcastle United crashed out of the English League Cup to Championship opposition in Wednesday's second-round games.
Liverpool beat Arsenal at Anfield in a penalty shootout on Wednesday after their last-16 tie ended 5-5 in regulation.
Timo Werner scored his first goal of the season as a much-changed Chelsea side crept into the fourth round of the League Cup by beating Aston Villa 4-3 on penalties after the Stamford Bridge clash ended 1-1 on Wednesday.
Ten Hag's contract was set to expire at the end of the 2024-25 season but denying Manchester City a domestic double and qualifying for the Europa League earned him another chance.
Holders Chelsea will meet Liverpool at Stamford Bridge in the quarter-finals of the League Cup next month.
Ipswich Town, thrashed 7-0 in the FA Cup by Chelsea three days ago, produced a memorable display to shock Arsenal 1-0 in the first leg of their League Cup semi-final at Portman Road on Wednesday.
Freezing temperatures and heavy snow have forced the postponement of this week's League Cup semi-final first leg matches.
Liverpool climbed to the top of the Premier League table with a 2-1 victory over struggling Wolverhampton Wanderers on Saturday.
Olympique Marseille became the first team to retain the French League Cup when a late Taye Taiwo goal gave them a 1-0 win over Montpellier in a scrappy final at the Stade de France on Saturday.
Images from the football matches played across Europe on Wednesday.
ManchesterCity beat Liverpool 3-1 on penalties to win the League Cup after Sunday's final finished 1-1 after extra time.
United rested several big names but were too good for Rovers at Old Trafford with Argentine striker Tevez running the show in a 5-3 victory in the only all Premier League clash of the quarter-finals. Tottenham, who beat Chelsea in the final last season, fell behind against Championship (second division) side Watford but hit back to win 2-1 at Vicarage Road.
'It is that I am, how can I say it, running out of energy.'
Tottenham Hotspur celebrated the return of England striker Jermaine Defoe on Tuesday by romping to a 4-1 semi-final first leg League Cup win over Burnley.
A controversial penalty three minutes into added time gave Paris St Germain a 2-1 win over fellow Ligue 1 strugglers Racing Lens in the French League Cup final at the Stade de France on Saturday.
Substitute striker Kris Boyd produced a sparkling performance to help Rangers beat Dundee United 3-2 in a penalty shootout and lift the League Cup on Sunday.
Manchester United manager Erik ten Hag will remain in the job for next season and has entered into talks with the Old Trafford club over a contract extension
French striker Jeremie Aliadiere fired Arsenal to a 3-1 extra-time victory over arch-rivals Tottenham Hotspur on Wednesday and a place in next month's League Cup final against Chelsea.
Andriy Shevchenko broke a seven-week drought on Tuesday with two goals which helped send champions Chelsea to the final.
Tottenham Hotspur defender Jonathan Woodgate scored the winning goal in extra-time as the north London upset the defending champions.
Liverpool will play Chelsea at Stamford Bridge twice in just over a week after the two Premier League teams were drawn to face each other in the quarter-finals of the English League Cup on Saturday.
Holders Manchester United will face Premier League rivals Wolverhampton Wanderers in the last 16 of the English League Cup after the draw was made on Saturday.
Manager Roberto Martinez described Romelu Lukaku as the perfect striker for Everton after the Belgian bagged his 19th goal of the season to secure a 2-1 win over Manchester City on Wednesday.
Goals from Freddie Hinds, Bobby Reid and Niclas Eliasson put the visitors through to the third round. Watford finished with 10 men after Jose Holebas was sent off.
Liverpool suffered a humiliating home defeat on penalties by League Two (fourth division) Northampton Town in the English League Cup third round on Wednesday.
Images from the League Cup matches played on Tuesday
Theo Walcott and Nicklas Bendtner made goalscoring returns from injury on Wednesday as Arsenal thrashed Newcastle United 4-0 away to reach the last eight of the League Cup.
Premier League clubs West Bromwich Albion and Watford were knocked out in the League Cup second round by lower-league opponents on Tuesday as a strong Liverpool side crushed championship Burton Albion 5-0.
The underdogs advanced through to the final on the away goals rule after a 2-2 aggregate scoreline against Arsenal.
Holders Manchester City held their nerve to beat Leicester City 3-1 on penalties and reach the League Cup semi-finals after an entertaining last-eight tie ended 1-1 on Tuesday.
The visitors' display was enough to earn them applause from their fans at the end.